What is a Prime Number? Easy Definition, Types, and Examples  

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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, it's a number that can only be divided evenly by 1 and itself.

Easy Definition:

A prime number is a whole number greater than 1 that is only divisible by 1 and itself.

Types of Prime Numbers:

1. Regular Prime: A prime number that is not a multiple of any smaller prime number.

2. Twin Prime: Prime numbers that have a difference of 2, such as 3 and 5, 11 and 13, or 17 and 19.

3. Mersenne Prime: Prime numbers that can be written in the form 2^p - 1, where p is also a prime number.

4. Fermat Prime: Prime numbers that can be expressed in the form 2^(2^n) + 1, where n is a non-negative integer.

5. Sophie Germain Prime: Prime numbers p such that 2p + 1 is also a prime number.

Examples of Prime Numbers:

2 is the smallest prime number.

3, 5, 7, 11, 13, and 17 are also prime numbers because they are only divisible by 1 and themselves.

4 is not a prime number because it can be divided evenly by 1, 2, and 4.

9 is not a prime number because it can be divided evenly by 1, 3, and 9.

11 and 13 are twin primes because their difference is 2.

Prime numbers are fundamental in mathematics and have many applications in fields such as cryptography, number theory, and computer science. They play a crucial role in the security of cryptographic algorithms and are used extensively in prime factorization and encryption techniques.